# csinf, csin, csinl

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< c‎ | numeric‎ | complex

Defined in header ``<complex.h>`` |  |
float complex csinf( float complex z ); | (1) | (since C99)
double complex csin( double complex z ); | (2) | (since C99)
long double complex csinl( long double complex z ); | (3) | (since C99)
Defined in header ``<tgmath.h>`` |  |
#define sin( z ) | (4) | (since C99)

1-3) Computes the complex sine of `z`.
4) Type-generic macro: If `z` has type long double complex, `csinl` is called. if `z` has type double complex, `csin` is called, if `z` has type float complex, `csinf` is called. If `z` is real or integer, then the macro invokes the corresponding real function (sinf, sin, sinl). If `z` is imaginary, then the macro invokes the corresponding real version of the function sinh, implementing the formula sin(iy) = i ∙ sinh(y), and the return type of the macro is imaginary.

### Parameters

z | - | complex argument

### Return value

If no errors occur, the complex sine of `z`.

Errors and special cases are handled as if the operation is implemented by -I * csinh(I*z)

### Notes

The sine is an entire function on the complex plane, and has no branch cuts.

Mathematical definition of the sine is sin z =

eiz -e-iz
2i

### Example

Run this code

    #include <stdio.h>
    #include <math.h>
    #include <complex.h>

    int main(void)
    {
        double complex z = csin(1);  // behaves like real sine along the real line
        printf("sin(1+0i) = %f%+fi ( sin(1)=%f)\n", creal(z), cimag(z), sin(1));

        double complex z2 = csin(I); // behaves like sinh along the imaginary line
        printf("sin(0+1i) = %f%+fi (sinh(1)=%f)\n", creal(z2), cimag(z2), sinh(1));
    }

Output:

    sin(1+0i) = 0.841471+0.000000i ( sin(1)=0.841471)
    sin(0+1i) = 0.000000+1.175201i (sinh(1)=1.175201)

### References

- C17 standard (ISO/IEC 9899:2018):

  - 7.3.5.5 The csin functions (p: 138-139)

  - 7.25 Type-generic math <tgmath.h> (p: 272-273)

  - G.7 Type-generic math <tgmath.h> (p: 397)

- C11 standard (ISO/IEC 9899:2011):

  - 7.3.5.5 The csin functions (p: 191-192)

  - 7.25 Type-generic math <tgmath.h> (p: 373-375)

  - G.7 Type-generic math <tgmath.h> (p: 545)

- C99 standard (ISO/IEC 9899:1999):

  - 7.3.5.5 The csin functions (p: 173)

  - 7.22 Type-generic math <tgmath.h> (p: 335-337)

  - G.7 Type-generic math <tgmath.h> (p: 480)

### See also

ccosccosfccosl (C99)(C99)(C99) | computes the complex cosine (function)
ctanctanfctanl (C99)(C99)(C99) | computes the complex tangent (function)
casincasinfcasinl (C99)(C99)(C99) | computes the complex arc sine (function)
sinsinfsinl (C99)(C99) | computes sine (\({\small\sin{x} }\)sin(x)) (function)
C++ documentation for sin

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